Speaking during a visit to Skopje, capital of the former Yugoslav republic of Macedonia, Mr Perry made it clear that no decision had been taken. But the Alliance would not simply "give up on the investment" that it had made in Bosnia. If Nato chose to stay, then the US should take part in the operation, "including ground troops".
The White House yesterday insisted that President Bill Clinton plans to stick with his timetable of basing US peace-keeping troops in Bosnia for "about a year".
President Clinton last night insisted that, as of now, he intends to stick to the original timetable. The Nato force could complete its mission "in about a year", at which point withdrawal would start, he said after a meeting with the European Commission President Jacques Santer, and Prime Minister Romano Prodi of Italy, current holder of the rotating European Union presidency. Mr Perry's remarks, the White House said, were "speculative".
Nonetheless they have lifted the lid off a topic which has mostly been shunned in public by both the European allies and Washington, for fear of turning it into a controversy in the US Presidential campaign.
And, taken with the recent statements of other senior American officials, they suggest that however unwelcome the prospect is, the administration is resigned to the fact that an extended Nato presence may be unavoidable.
From the outset, the 1995 Dayton peace accords were tailored to minimise the political risk to President Clinton, ensuring that the 18,000 US troops would remain in Bosnia until well after the vote on 5 November, ensuring no flare-up of fighting during the campaign. By and large, the strategy has worked.
US casualties have been very few, an uneasy peace has been kept and Bosnia has not featured in the campaign, not least because Mr Clinton's Republican opponent, Bob Dole, supported the deployment of US forces.
But, indirectly, the argument has resurfaced, as the US has exerted strong pressure for Bosnia's first post-war elections to be held on schedule by 14 September, even though the conditions stipulated by Dayton, including a free press, an end to human rights abuses and the return of refugees to their homes, have not been met. The Bosnian Serb leaders, Radovan Karadzic and Ratko Mladic, who have been indicted for war crimes, are still at large.
Despite the US argument that the elections will help to rebuild Bosnia, several of Washington's allies, as well as the Organisation for Co-operation and Security in Europe (OCSE), the body supervising progress towards elections, believe Bosnia is not ready. Washington's stance, they suspect, is driven by domestic politics.
Hence Mr Perry's gambit, designed to show that the US will not demand adherence to the Dayton timetable. Some diplomats here believe it was timed for the meeting in Florence of parties to the Bosnian conflict.
According to Mr Perry, the continued presence of US and other Nato ground troops is only one post-December option to be considered. Others include the continued threat of massive Nato airpower to preserve the peace, or the deployment of a rapid-reaction force close by.