First Minister Alex Salmond has set out plans to scrap tolls on the Tay and Forth road bridges as part of his programme for running Scotland.
A timescale for scrapping the tolls has yet to be set out
The SNP, which has branded the charges "unacceptable and unfair", promised to introduce a bill to abolish them within 100 days of taking office.
Mr Salmond set out his plans in a statement to the Scottish Parliament.
However, his minority administration will need to gain the support of other parties to get the proposals through.
Mr Salmond told MSPs: "I know and understand that this move is not universally supported in this chamber, but I believe it can carry - and should carry - majority support."
He added: "We shall see".
Scottish Labour transport spokesman Des McNulty offered "constructive" support to the abolition of tolls on the Forth and Tay bridges, but stressed the need to tackle congestion and address the requirement for a new Forth crossing.
The timescale for scrapping the tolls is expected to be set out shortly.
The previous Scottish Executive scrapped tolls on the Erskine Bridge over the Clyde, saying the move would ease congestion on river crossings in nearby Glasgow.
The new government also wants to scrap tolls on the Tay Road Bridge
But the then Transport Minister Tavish Scott had argued that removing the Forth and Tay tolls could have the opposite effect, while increasing carbon emissions at the same time.
That executive also abolished the controversial Skye Bridge charges, after buying it back from its private owners for £27m.
A spokesman for the campaign group, the National Alliance Against Tolls Scotland (Naats), said: "If the removal of the tolls is confirmed those who have campaigned many years for this will be over the moon.
"It will remove an injustice for those in Fife and on Tayside. It will also benefit the rest of Scotland, as declaring a toll-free nation will be a boost to tourism and inward investment."