House Speaker John Boehner (R-Ohio) on Wednesday sent a letter to President Obama in which he said he and other members are concerned that key questions about the U.S. mission in Libya remain unanswered.

Meanwhile, House Minority Leader Nancy Pelosi (D-Calif.) issued a brief statement of support for Obama on Libya but sounded a more cautious note than a trio of top Senate Democrats who earlier Wednesday defended the administration’s actions.

In his letter to Obama – which was released just as the president arrived at Andrews Air Force Base from El Salvador — Boehner told him, “I respect your authority as Commander-in-Chief and support our troops as they carry out their mission.”

But Boehner added that he “and many other members of the House of Representatives are troubled that U.S. military resources were committed to war without clearly defining for the American people, the Congress, and our troops what the mission in Libya is and what America’s role is in achieving that mission.

“In fact, the limited, sometimes contradictory, case made to the American people by members of your Administration has left some fundamental questions about our engagement unanswered,” Boehner wrote. “At the same time, by contrast, it appears your Administration has consulted extensively on these same matters with foreign entities such as the United Nations and the Arab League.”

Boehner then followed with a list of seven bullet points, each containing several questions about the U.S. role in Libya.

One question deals with whether it would be an “acceptable outcome” for Libyan leader Moammar Gaddafi to remain in power after the international military intervention concludes; another asks what the U.S. military role will be if coalition partners disengage from the mission.

Boehner also requests a more detailed timeline on the transition of control to coalition forces and asks Obama for a ballpark figure on the cost of the military operation.

The final item on the list poses what Boehner calls a “fundamental question” to Obama: “What is your benchmark for success in Libya?”

Pelosi, meanwhile, expressed support for the White House in her statement but emphasized the need for continued consultation between the president and Congress.

“Actions taken by the international community have already prevented [Gaddafi] from implementing his threat to ‘show no mercy’ to his own people, including those living in the city of Benghazi,” Pelosi said. “Decisions made in the days ahead are strengthened by our NATO partners’ participation. U.S. participation is strengthened by the President’s continued consultation with Congress.”

The statements from both leaders come as rank-and-file lawmakers have increasingly criticized the White House on Libya, expressing concern that Congress’s role in the decision-making process has been overlooked or criticizing what they say is a lack of clarity on the U.S. mission.

Also on Wednesday, Sen. Dick Lugar (R-Ind.), the top Republican on the Senate Foreign Relations Committee, wrote a letter to Senate Foreign Relations Chairman John Kerry (D-Mass.) requesting that the committee take up discussion on Libya when Congress returns next week.

"I wanted to make clear that I believe prompt hearings on Libya in our Committee are essential," Lugar wrote. "Any U.S. military intervention in a foreign country would require oversight hearings by the Foreign Relations Committee.  In my judgment, hearings on Libya are especially vital because the Obama Administration did not consult meaningfully with Congress before initiating military operations."

Congress is on a week-long recess, but lawmakers are already making moves toward addressing the Libyan crisis either through legislation or in committee hearings. In the meantime, some continue to spar with the White House from a distance. With Obama now back in the country following a trip to Central and Latin America, and the Libyan conflict currently on its fifth day, such exchanges are likely to intensify.

This post has been updated since it was first published.