TUCSON (Arizona) - UNITED States President George W. Bush and Iraqi Prime Minister Nouri al-Maliki have agreed to set a 'time horizon' for US troop withdrawals as part of a long-term security pact, the White House said.

But any reduction in the US force presence 'would be based on continued improving conditions on the ground and not an arbitrary date for withdrawal', spokesman Dana Perino said in a statement on Friday.

The two leaders, speaking by videoconference on Thursday, also settled on a 'common way forward' in stumbling talks to craft a long-term pact governing diplomatic ties and the US military presence, said Ms Perino.

But the talks have sputtered over the Baghdad government's demands for a timetable for US troops to withdraw as well as Washington's demands that its soldiers and other staff be immune from Iraqi prosecution.

In their latest talks, 'the leaders agreed on a common way forward to conclude these negotiations as soon as possible', Ms Perino said in a statement that made no mention of Mr Bush's hopes that the accord would be sealed in July.

They also agreed that the pact would 'include a general time horizon for meeting aspirational goals - such as the resumption of Iraqi security control in their cities and provinces and the further reduction of US combat forces from Iraq', she said.

The announcement came at a pivotal time in the US presidential campaign, with Democratic candidate Barack Obama expected to visit Iraq soon amid Republican rival John McCain's attacks on his plan for pulling US combat forces out of Iraq within 16 months after the White House changes hands in January.

Mr McCain said the agreement on a 'time horizon for American troop presence is further evidence that the surge (of additional US troops into Iraq begun last year) has succeeded', noting that most US forces used in the surge have already been withdrawn.

'When a further conditions-based withdrawal of US forces is possible, it will be because we and our Iraqi partners built on the successes of the surge strategy, which Senator Obama opposed, predicted would fail, voted against and campaigned against in the primary,' he said in a statement.

Mr Obama's campaign spokesman Bill Burton described Friday's announcement as 'a step in the right direction', but said it was now 'time to pressure Iraq's leaders to reach the political accommodation necessary for long-term stability, and to refocus on strengthening our military and finishing the fight in Afghanistan'.

Where the White House referred to reducing troop levels, not quitting Iraq entirely, Iraqi government spokesman Ali al-Dabbagh said the goal was 'to decrease the number of American forces in Iraq and later withdraw them'.

Ms Perino said US forces would move 'from a primary combat role' to what Washington calls an 'overwatch role' of training and advising Iraqi forces, and carrying out special forces operations.' -- AFP