WASHINGTON — The senior allied commander in Afghanistan suggested on Thursday that he might not advocate any further drawdown of the American force in Afghanistan going into 2013 once the so-called surge forces ordered by President Obama leave this fall.

In testimony before the Senate Armed Services Committee, the commander, Gen. John R. Allen of the Marines, made his most direct comments to date about whether he might advocate a freeze on troop withdrawals despite political pressures for a quicker exit.

General Allen stressed, however, that he would not even begin his formal assessments until he could review the security situation on the scene at the conclusion of the summer fighting season. At that point, the 33,000-strong “surge” force is scheduled to withdraw, leaving about 68,000 American service members in Afghanistan.

That timeline would put off the debate on troop levels until after the November presidential election. The pace of reducing American forces in Afghanistan looms as a partisan issue ahead of the election, although both Democrats and Republicans have endorsed an agreed-upon timeline under which the NATO mission in Afghanistan would come to a close at the end of 2014. There are about 40,000 allied troops in Afghanistan in addition to the American deployment.