WASHINGTON — Former President George W. Bush implicitly criticized President Trump on Monday, taking issue with his approach to immigration and the news media, and suggested that any ties between the new president’s team and Russia should be investigated.

In a television interview to promote a new book of his paintings, Mr. Bush indicated that important questions were raised by reported contacts between Russian officials and Mr. Trump’s associates during last year’s election campaign. Mr. Trump forced out his national security adviser for withholding information about a call with Russia’s ambassador.

“I think we all need answers,” Mr. Bush said on the “Today” show on NBC. He said he would defer to Senator Richard M. Burr, Republican of North Carolina and chairman of the Senate Intelligence Committee, about how such an investigation should be conducted. He is a “really good guy, and an independent thinker,” Mr. Bush said of Mr. Burr, “and if he were to recommend a special prosecutor, then it would have a lot more credibility with me.”

Like other members of his family, Mr. Bush did not support Mr. Trump during last year’s campaign against Hillary Clinton, although in public he largely kept his views to himself. Mr. Bush congratulated Mr. Trump after his victory and attended the inauguration last month, but the interview on Monday made clear that the most recent Republican president still had serious disagreements with his party’s incumbent commander in chief.