Mr Blair, who was elected the party's leader 20 years ago following the death of John Smith, said there was a sense of optimism about Better Together and its arguments for keeping Scotland in the UK.
The No campaign is led by Alistair Darling, who held a string of cabinet posts under Mr Blair, before rising to Chancellor under Gordon Brown.
Mr Blair, who defeated John Prescott to the Labour leader- ship on July 21, 1994, has kept a low-profile in the independence campaign, with few public pronouncements on the issue.
His Government set up the referendum on devolution that was backed by voters in September 1997 and led to the creation of the Scottish Parliament.
His latest comments, which followed a wide-ranging speech to New Labour think-tank Progress, have been described as "a huge embarrassment for the No camp" by the SNP.
When asked if Better Together and the Labour leadership had done enough to save the Union, Mr Blair said: "I hope so, I believe so.
"I think the arguments of the Better Together campaign have got stronger as time has gone on. We will see."
He said "there is a sense of optimism" about Better Together.
SNP Westminster leader Angus Robertson said: "Getting the support of Tony Blair on the day it is reported he is to receive a warning letter from the Chilcot Inquiry as the architect of the illegal war in Iraq can only be a huge embarrassment for the No camp.
"Mr Blair has been kept well away from the referendum debate by the No campaign for obvious reasons, until now. His illegal war in Iraq was a calamity, and an avoidable one at that, and the people of Scotland will not forget it.
"Only with a Yes vote in September can Scotland avoid any future illegal Westminster wars and decide a foreign policy based on Scotland's interests."
Mr Blair also warned his party would not regain power campaigning on a platform of abandoning markets and a return to more state control,
He said the global financial crash of 2008 did not mean people had "fallen back in love" with the state or that the whole private sector was "contaminated".
Mr Blair said Labour needed to adopt the same "iconoclastic" approach to re-shaping public services that he adopted when he first became party leader.
"When we look at the Britain of 2014, we should be the radicals, but the radicals not playing to the gallery of our ideological ghosts but to the contemporary stadium of the progressive majority," he said.
Mr Blair endorsed Ed Miliband's commitment to achieving greater value for money from public services in the aftermath of the financial crash.
At the same time, however, he said the party needed to remember the lesson of the 1990s that the public would not accept a programme predicated on a greater role for the state.
"What the financial crisis does not alter is as important as what it does. It does not mean people have fallen back in love with the state; it does not mean the individualising force of technology has retreated and it does not mean the whole private sector is somehow contaminated," he said.
l Labour has widened its lead over the Tories, according to the latest weekly opinion poll by Conservative peer Lord Ashcroft. The Ashcroft National Poll, which questioned about 1,000 adults, put support for the Conservatives on 27% - down five points on last week - leaving them eight points adrift of Labour, which is down one on 35%.