WASHINGTON — Turkey is continuing to push the Obama administration to impose a no-fly zone or safe area along the Turkish-Syrian border, administration officials said Monday, but obstacles remain to the United States’ committing to what would be a significant increase in American military engagement in the area.

The administration has not ruled out establishing a no-fly zone over northeastern Syria to protect civilians from airstrikes by the Syrian government, as President Recep Tayyip Erdogan of Turkey has been requesting for months. But administration officials say they have not yet reached an agreement with the Turks on a plan.

“There have been ongoing discussions about a range of proposals that Turkey has put forward, and they have taken many forms,” a State Department spokeswoman, Jen Psaki, told reporters on Monday. “But we continue to have differences and haven’t made a decision about a specific course of implementation.”

The White House press secretary, Josh Earnest, also played down news reports that the United States was close to acceding to Turkey’s request and was negotiating an “air-exclusion” zone inside Turkey that would be policed by Turkish troops and enforced by American air power.