President-elect Donald J. Trump filled two lower-profile but influential White House staff jobs on Friday, while his high-profile candidate for secretary of housing and urban development, Ben Carson, continued to deliberate about whether to join the administration.

Mr. Trump offered the housing job this week to Mr. Carson, a neurosurgeon who challenged him for the Republican presidential nomination. But despite expectations of a Friday announcement, Mr. Carson was “still pondering,” said a friend, Armstrong Williams. The president-elect’s aides said Mr. Trump did not plan any more cabinet-level announcements until next week.

For the politically sensitive post of White House counsel, Mr. Trump chose Donald F. McGahn II, a Washington election lawyer who pushed to deregulate campaign finance and election laws. The counsel’s job may be even more daunting than it was in previous administrations, given Mr. Trump’s far-flung business empire, with which he shows no inclination toward severing ties.

For the equally critical job of deputy national security adviser, Mr. Trump chose K. T. McFarland, an aide in three Republican White Houses and a Fox News commentator. She has been highly critical of President Obama’s approach to combating terrorism — a view that aligns her with Mr. Trump’s choice for national security adviser, Lt. Gen. Michael T. Flynn.

In rolling out the appointments, the Trump transition team lined up testimonials from big names in both parties.

Former Senator Joseph I. Lieberman, regarded as a foreign policy hawk, praised Ms. McFarland, 65, as “one of our country’s most experienced, informed and wise foreign policy and national security experts.” Mr. Lieberman, a Connecticut Democrat turned independent, was a Yale College and law school classmate of Ms. McFarland’s husband, Alan R. McFarland, a well-known investment banker.

Edwin Meese III, an attorney general under President Ronald Reagan, said Mr. McGahn, who was the general counsel for the Trump campaign, had “dealt ably with the intersection between politics, government ethics and the rule of law.” C. Boyden Gray, a White House counsel to the elder President George Bush, said Mr. McGahn was well suited to the job because of his “serious prior relationship with the president” and his “working knowledge of government ethics and election law.”