WASHINGTON — The Obama administration is considering keeping a force of 3,000 to 9,000 troops in Afghanistan after 2014, American officials said Saturday.

The new options under consideration are smaller than the 6,000 to 20,000 troops Gen. John R. Allen, the American commander in Afghanistan, is said to have previously suggested.

These potential alternatives were produced by the Pentagon at the behest of the White House and reflect a familiar pattern within the Obama administration on the use of force. Sensitive to public opinion and budgetary pressures, the White House has generally favored lower troop levels during its previous deliberations on Afghanistan and Iraq.

The military, by contrast, has tended to favor somewhat higher numbers, because of the greater risks posed by a smaller force carrying out its mission in a rugged and hostile environment like Afghanistan. In this case, the Pentagon believes that the 9,000-troop option — the upper range of the new scale — is more realistic, officials said.