David Jackson

USA TODAY

After bashing President Obama over Israel and transition issues — but then saying they had a nice phone conversation — Donald Trump and aides on Wednesday floated the idea of creating a new "public-private" system for veterans health care.

Amid a series of job interviews, Trump met with a group of health care professionals in a discussion that included talk of a system that would allow veterans to use the traditional VA system or opt for private medical facilities.

"Definitely an option on the table to have a system where potentially vets can choose either/or, or all private," said one senior transition official, speaking on condition of anonymity because nothing has been formalized.

Trump has not yet named his choice to head the VA, an agency that has been rocked by scandal since it was revealed in 2014 that veterans were dying while waiting for long-delayed medical appointments. The VA secretary was replaced and the agency has made a major emphasis on improving care, but USA TODAY earlier this month published documents showing that effort is achieving mixed results.

The group that met with Trump Wednesday included Cleveland Clinic CEO Delos "Toby" Cosgrove, rumored to be under consideration to be Trump's pick for VA secretary. The official said it is possible the group could become a standing advisory committee on veterans health care, though that also has not been decided.

Trumpo The new VA concept emerged hours after the president-elect criticized Obama over Israel and transition issues, but said later that he had a "nice" and "general" conversation with his predecessor, though he did not provide details.

"He phoned me — we had a very nice conversation," Trump told reporters after also announcing that two companies, Sprint and OneWeb, have pledged to create a total of 8,000 new domestic jobs.

The jobs are returning into the United States, "which is a nice change," said Trump, who during the presidential campaign claimed the U.S. was losing jobs because of bad trade deals with other countries. Neither Trump nor the companies provided any detail about the jobs.

Trump began his day by Twitter-trolling Obama over Israel, the United Nations, and the transition in general.

"Doing my best to disregard the many inflammatory President O statements and roadblocks," Trump tweeted. "Thought it was going to be a smooth transition - NOT!"

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Trump did not cite specifics, but he followed up with tweets criticizing the Obama administration for refusing to veto a United Nations resolution criticizing Israel over settlements on land disputed with the Palestinians.

"We cannot continue to let Israel be treated with such total disdain and disrespect," Trump said.

He added: "They used to have a great friend in the U.S., but not anymore. The beginning of the end was the horrible Iran deal, and now this (U.N.)! Stay strong Israel, January 20th is fast approaching!"

Later in the day, Trump appeared to walk back his criticism of the transition, telling reporters it is going "very, very smoothly, very good. You don't think so?"

The White House confirmed the Obama-Trump conversation on Wednesday. "Today's call, like the others since the election, was positive and focused on continuing a smooth and effective transition," said spokesman Eric Schultz.

The Trump tweets on Israel preceded a speech by Secretary of State John Kerry laying out the outgoing Obama administration's vision for Middle East peace and pushing back at the administration's critics.

Israeli Prime Minister Benjamin Netanyahu, who has had a tense relationship with Obama, responded to Trump on Twitter, saying: "President-elect Trump, thank you for your warm friendship and your clear-cut support for Israel."

Members of the Obama administration, meanwhile, have questioned Trump's involvement in the Israel dispute. "There's one President at a time," said deputy national security adviser Ben Rhodes last week. "President Obama is the President of the United States until January 20th."

Trump declined to critique Kerry's speech, telling reporters "it speaks for itself."

Trump plans to remain at Mar-a-Lago this week, returning to New York City on New Year's Day on Sunday.

Stay with USA TODAY for full coverage of the 2017 inauguration.