Home Secretary Theresa May's scheme was due to be piloted from this month as a way of deterring temporary visitors from staying on in the UK after their visas expire.
It had been suggested that visitors from India, Pakistan, Sri Lanka, Bangladesh, Ghana and Nigeria would be required to pay the deposit for a six-month visa, but it is understood the scheme has now been scrapped.
A Government spokesman said: "The Government has been considering whether we pilot a bond scheme that would deter people from overstaying the visa. We have decided not to proceed."
Earlier this year, the scheme was condemned as ''highly discriminatory'' by Indian business leaders and Nick Clegg indicated he would block the plans if they were applied in an "indiscriminate way".
Mr Clegg told BBC1's Andrew Marr Show: ''Of course in a coalition I can stop things'', and added: ''I am absolutely not interested in a bond which becomes an indiscriminate way of clobbering people who want to come to this country, and in many respects bring great prosperity and benefits to this country, of course not."
The scheme was part of the Government's drive to cut net migration into the UK to the ''tens of thousands'' by the time of the next general election in 2015.
However, the Confederation of Indian Industry (CII) denounced the plan as ''highly discriminatory and very unfortunate'', warning that it could delay agreement on an EU-India trade deal.
''The suggested changes are not only discriminatory they are also against the 'special relationship' publicised by the UK government.
"We share UK's concern on illegal immigration but surely there are other more effective and non-discriminatory ways to put a check on it,'' it said in a statement.
Their complaints were echoed by the chairman of the Commons home affairs select committee, Labour MP Keith Vaz, who described the scheme as ''unfair and discriminatory''.
''This flies in the face of the Prime Minister's intention to attract the brightest and best to Britain and sends out the wrong message to the countries concerned," he said.
Mr Vaz added: "The Home Secretary is right to shelve the bond proposals. At the time she announced the pilot I warned her that bonds would not work.
"During this shambolic process the Home Office has managed to upset a number of foreign governments and confuse millions of potential visitors.
"This is not the way to fashion a strong and effective immigration policy."
Shadow Immigration Minister David Hanson said: "After ad vans and texts to the wrong people, it seems David Cameron's Government can't get anything right when it comes to dealing with illegal immigration.
"Theresa May is all over the place and presiding over an immigration policy in chaos.
"Within a week of the Home Office briefing that they would be introducing £3,000 bonds for family visitors to the UK from 'high risk' countries the policy was briefed against by No10 and now it is officially dead and an ex policy.
"Investors in India are now put off from investing in the UK whilst the Home Office fail repeatedly to do anything about their failure at our borders to stop and return illegal immigrants, failure to tackle backlogs in processing delays or enforcement of immigration rules within the UK.
"Chasing headlines followed by confusion and U turn is no way to manage an effective and robust immigration policy that works for all concerned."
The bonds were dropped because they had no support from the Liberal Democrats or within a number of government departments, it was claimed.
Among the departments understood to be opposed to the plans are the Foreign Office, Department for Business, Innovation and Skills, and the Department for Communities and Local Government.
"The Home Office version of the policy was not acceptable to the Liberal Democrats and was not support by other government departments," Lib Dem sources said.
"They have seen the writing on the wall and binned it off.
"We have been clear from the start that the version was just not acceptable to us."