The figure for new pensioners would at least match any higher UK Government provision, currently estimated to be £158.90 in the same year.
The commitment is made in a report entitled Pensions in an Independent Scotland, published today.
The SNP Government, assuming a Yes vote next September, promises to continue paying the basic state pension at the current rate of £110.15 a week, which it says is expected to rise to at least £118.60 in 2016-17.
Ministers would keep the "triple-lock" to ensure the pension keeps pace with earnings and rising costs, at least for the first term of an independent parliament in Edinburgh.
Safeguards would be put in place for people, mainly women, who are expecting to receive a state pension based on their spouse's contributions, the Scottish Government said.
An expert commission would be established to consider the appropriate age threshold for pensions.
Deputy First Minister Nicola Sturgeon said: "Scotland is a wealthy and productive country with strong financial foundations.
"We can more than afford a decent pensions system that guarantees dignity for our older people.
"Successive UK Government decisions have resulted in a pensions crisis. Independence will bring decision-making on pensions home to the Scottish Parliament and provide the opportunity to do things differently and better.
"As this comprehensive paper makes clear, we will build on the current system and make improvements where necessary.
"We are giving an absolute guarantee to those living in Scotland, in receipt of the UK state pension at the time of independence, that their pensions will continue to be paid in full and on time, as now.
"We will also take steps to protect lower income pensioners by ensuring that pensions hold their value against prices and earnings, and by retaining savings credit.
"For those approaching retirement, the paper provides clarity about their future state pension terms and sets out how they would be better off with independence.
"We will also establish an expert commission to review the current, accelerated UK timetable for the State Pension Age and consider the appropriate pace of change to the retirement age beyond 66, taking full account of Scottish circumstances."
The UK Government proposes increasing the age at which people start to receive their state pension, with this planned to rise to 66 for both men and women from 2018 and to 67 from 2026.
The Department for Work and Pensions (DWP) has said not increasing the state pension age to 67 in Scotland in 2026 could cost the country £200 million in the first year alone - and this could rise to £800 million by 2030.
Ms Sturgeon accepted: "If you were to delay it by a year, the first year, it would be in the region of £200 million."
When asked how much it would cost if the state pension age in Scotland did not increase to 67 in line with the rest of the UK, the Deputy First Minister said: "That depends on what recommendation you have in terms of how many years you would delay that, that's what we're asking an expert commission to do, to look at the Scottish circumstance to see if we should delay it beyond 2026 and if so for how many years."
Previous plans meant the state pension age would not be increased to 67 until 2035, Ms Sturgeon said, adding that SNP ministers were "not persuaded that the increase to 2026 is the right pace of change".
Instead she said: "The right and responsible thing to do if we have independence is to get the ability to look at that in detail to see what the correct pace of increase would be."
With life expectancy lower in Scotland than the UK average, Ms Sturgeon argued: "Why should people in Scotland who pay in the same contributions to pay for pensions on average get less out of that because we have a lower life expectancy in Scotland?
"We have to have the ability to determine what is the correct pace of change in Scotland, rather than have that decision taken almost regardless, or completely regardless, of specific Scottish circumstances."
The Deputy First Minister spoke out on the issue as she visited residents at a sheltered housing complex in Glasgow.
Finance Secretary John Swinney joined her for the visit, with the pair chatting to pensioners.
Mr Swinney insisted pensions would be affordable if Scotland were to become independent.
He said pensions costs "account for a smaller proportion of the taxes of the size of the Scottish economy than they do for the rest of the UK", and added: "That essentially creates the context around which the commitments which we make are affordable."
He went on: "Although our population is aging, our population is not aging as fast as is happening in the rest of the UK. One of the key issues that arises out of that is how we utilise the powers of independence to create more dynamic economic opportunities to encourage more and more working age people to live and work in Scotland, and that's a key part of our economic strategy."
Mr Swinney also stressed the importance of "making sure you run the public finances in an effective and sustainable fashion to enable you to deliver your commitment".
He said: "That has been the attitude of mine we have brought to the way we have exercised our responsibilities as the devolved government of Scotland. That attitude of mine would be no different under independence.
"But what you would have in an independent Scotland would be the ability to use a range of other economic levers to strengthen the economic position of Scotland."
When pressed on the cost of pensions, Ms Sturgeon said: "We've been told since day one of our government that we couldn't afford to do the things we had committed to doing. John has proved them wrong every single year in prioritising the areas where we want to spend money and delivering a balanced budget.
"And it's exactly that kind of fiscal discipline we would take into an independent Scotland as well."
She said the Scottish Government report "sets out a firm foundation for pensions in an independent Scotland", saying it was all "carefully thought through, carefully considered, both in terms of affordability and what is right for Scottish circumstances".
But a DWP spokesman said yesterday: "Spending on pensions, on benefits and on public services is all more affordable as part of the UK. Everyone benefits from the same UK-wide welfare and pensions system, which treats people equally regardless of where they live.
"Pensions spending per head is already higher in Scotland than in the rest of the UK, and in future Scotland will have a higher proportion of elderly people. But by pooling our resources, we won't need to rely on volatile and declining North Sea revenues to pay the pensions of Scotland's elderly."
Meanwhile the pro-union campaign group Better Together said the cost of not increasing the age people receive the state pension at to 67 could amount to £6 billion over the period 2012-27 to 2035-36.
Labour pension spokesman Gregg McClymont said: "Leaving the United Kingdom would be costly and risky for pensions."
"Barely a day now goes by without the nationalists making promises without any plan to pay for them, but this latest suggestion on state pensions would cost Scotland £6 billion."