The Obama administration is quietly ramping up pressure on Saudi Arabia to stop bombing Iran-backed rebels in Yemen and engage in peace talks toward a political solution to the nation’s conflict.

While Pentagon officials have said they are still backing the now month-old Saudi bombing campaign against on Houthi rebel targets in Yemen, the White House is increasingly signaling a desire for the campaign to come to an end.

“There is no military solution to the crisis in Yemen, and the humanitarian situation will only worsen if the conflict continues,” President Obama’s National Security Adviser Susan E. Rice said on Wednesday night.

Speaking before the Arab American Institute’s Annual Kahlil Gibran Gala in Washington, D.C., Mrs. Rice said the administration is “working with all parties to end the violence so that U.N.-led political negotiations can resume promptly and humanitarian access can be restored.”

Her comments underscored the sensitive diplomatic line being toed by the administration the Middle East, where the region’s main Sunni Arab powers — namely Saudi Arabia — are wary of Washington’s growing closeness to Iran.

On one hand, the administration is pushing for a major detente with Iran through the ongoing pursuit of a nuclear deal with Iranian leaders. On the other, the administration is backing the Saudi Arabia’s war against the Iran-backed rebels in Yemen.

The situation is further complicated by ongoing violence in Iraq, where the administration appears to be working tacitly with Shiite Muslim Iranian proxy forces in a war against the Islamic State — an extremist Sunni Muslim terrorist group.

In a show of the fragility around the mix of conflicting alliances, officials from Saudi Arabia and Iraq traded barbs publicly in Washington two weeks ago over Riyadh’s campaign against Iran-backed rebels in Yemen.

A day after meeting with Mr. Obama, Iraqi Prime Minister Haider al-Abadi slammed the U.S.-supported campaign, saying it has “no logic” and warning it could explode into a regional sectarian war between Iran-backed Shiites and Sunni factions aligned with the Saudis.

The remarks had barely made headlines when Saudi Arabia’s ambassador to Washington — holding his own press conference to tout successes of the campaign in Yemen — shot back that it was Mr. Abadi’s claims that had “no logic.”

At the time, Ambassador Adel al-Jubeir, who has since been elevated to the position of Saudi foreign minister, said Riyadh does want a political solution in Yemen, but only after the Iran-backed Houthis fully demilitarize and withdraw from the nation’s capital.

“There can be no half measures,” the ambassador said when pressed for an assessment of how long the Saudi-led campaign against the Houthis may last.