"All parties should return to the negotiating table immediately and resume discussion in good faith on the basis of Secretary-General (Kofi) Annan's Cyprus settlement plan," Bush said in letters to the three leaders.
He noted that Annan would only resume mediation if all parties "express the political will to finalise the plan and put it to referenda".
"I urge you to follow this approach, which the (UN) Security Council has unanimously endorsed," he added.
Greek Prime Minister Costas Simitis and Cypriot President Tassos Papadopoulos have welcomed receipt of their letters, sent late last month.
However, Turkish Prime Minister Tayyip Erdogan, who will meet Bush in Washington on 28 January, has not yet acknowledged his letter.
Pressure on Turkey
Cyprus was partitioned in 1974 when Turkish forces took over the northern part of the island in response to a coup in Nicosia engineered by the junta then ruling Greece.
"We have a window of opportunity to reach agreement before Cyprus joins the EU on 1 May, which would be in the strategic interests of both Turkey and the United States"
United States President
Only Turkey recognises the Turkish Cypriot state and maintains around 35,000 troops there.
Turkey has been under tremendous pressure to break the stalemate before the Greek Cypriot government joins the European Union on 1 May.
Brussels has warned Turkey that its own hopes of joining the EU would be harmed if it failed to push the Turkish Cypriots into some kind of deal.
"We have a window of opportunity to reach agreement before Cyprus joins the EU on 1 May, which would be in the strategic interests of both Turkey and the United States," Bush wrote to Erdogan.
Turkey's ambassador to Washington, Osman Faruk Logoglu, said on Wednesday that his government hoped to agree soon on proposals making "limited but important" changes to the UN plan.
But Turkish media has reported that influential generals feared Ankara was making too many concessions.
The UN has been trying for years to reunite Cyprus as a bi-zonal, bi-communal federation, as stipulated in Security Council resolutions.
Rauf Denktash has said that he
prefers a confederation
Veteran Turkish Cypriot leader Rauf Denktash has sought a confederation, a much looser form of union than a federation, to link two independent states.
The letters to the Greek and Cypriot leaders expressed similar sentiments to the one sent to Turkey.
Bush, in his letter to Simitis, said Greece should encourage Papadopoulos to return to the negotiating table immediately and noted that the Cypriot leader had said he would do so.
"Now is the time for action," Bush wrote.
To Papadopoulos, Bush said that his leadership would be "essential to reaching a comprehensive, lasting agreement" in pursuit of an "historic settlement".
Ankara promises deal
Turkey said on Thursday that it would soon announce its vision of a deal to end a decades-long problem.
Prime Minister Erdogan held all-day talks with the president, foreign minister, army chief and Turkish Cypriot political leaders, but said a final decision on Turkey's stance would have to wait the meeting of the influential National Security Council at the end of the month.
"We will evaluate all the work we have done so far in the council's meeting on 23 January and the government will annnounce its roadmap,"
Erdogan told reporters after the talks.
He gave no details as to what the roadmap would contain, but officials in Ankara have been working on peace proposals based on a UN-brokered plan to re-unite the island - categorically opposed by Turkish Cypriot leader Rauf Denktash.
"Turkey continues its support for the good offices of the UN
secretary general and confirms its political determination for the speedy achievement of a settlement based on the realities of the island through negotiations," said a statement issued after the prime minister's discussions.