Pakistan stopped the convoys in protest at US air strikes which killed 24 of its troops at two checkpoints on the Afghan border last month.
Mr Gilani refused to rule out closing Pakistan’s airspace to the US.
He also denied rumours President Asif Ali Zardari had suffered a stroke and the army was trying to oust him.
Mr Gilani said Mr Zardari was making a rapid improvement in hospital in Dubai, but would need two weeks’ rest before returning home.
The air strikes on 26 November marked a low point in relations between Washington and Islamabad, which have long been strained by the US-led military campaign against militants in Afghanistan.
In a wide-ranging interview with the BBC, Mr Gilani said Pakistan and the US needed to trust each other better.
“Yes there is a credibility gap, we are working together and still we don’t trust each other,” Mr Gilani said.
Mr Gilani also said he would investigate the blocking of the BBC’s international news TV channel, BBC World News, by Pakistani cable television operators. Operators say the move is in response to a documentary broadcast by the channel entitled Secret Pakistan.