House Minority Leader John A. Boehner says Republicans will continue their rump House sessions for at least two more weeks.

“The nationwide House GOP energy protest is making history, and we are writing to announce that the Call to Arms will continue,’’ Boehner said Thursday in a memo to the other 198 House Republicans.

GOP members were expected to hold another impromptu floor gathering on Thursday, as part of their ongoing effort to pressure Speaker Nancy Pelosi into calling all House members back to deal with sky-high gas prices.

Boehner asked Republicans to indicate if they are available from Aug. 11 to Aug. 22 to take turns leading the highly unusual sessions, which began when the House formally adjourned on Aug. 1.

“We must build on this opening, and keep building on it until the American people have been heard,’’ Boehner added.

The plan would almost cause the protest sessions to bump up against the Democratic National Convention, which opens in Denver on Aug. 25.

Pelosi has scorned the GOP effort, saying that Republicans who call for more offshore drilling are missing the boat on several counts. She and her fellow Democratic leaders point out that there are already some 83 million acres of federally owned land and offshore acreage already available for oil and gas production leases but that aren’t being used.

Her office also points out that while Republicans are now talking about an “all of the above’’ energy strategy many of their leaders have voted against what Democrats say were proposals to boost conservation, alternative energy and crack down on oil market manipulation.

Republicans feel they have scored solid political points by tapping into public anger over gas prices that peaked nationally at more than $4 a gallon before subsiding in the last few weeks.

The sessions are taking place with the chamber’s microphones and TV lights off, but members have been spreading information — including short videos — online.

On Wednesday, GOP members were joined by former Speaker Newt Gingrich, R-Ga. (1979-1999), who said he sensed they were gaining momentum in winning Democratic allies. Gingrich also said he believed Republicans would get the vote they want on an expansion of oil drilling in September.