Leaders discussed their prospective contacts with new US administration during a wide-ranging video call, Kremlin says.
At a hearing, Elise Stefanik pledged to continue the US's defence of Israel and advance Trump's 'America First' agenda.
In a speech on Tuesday, Rubio defended his department's employees but warned of alterations to come under Trump.
Linda Fagan, the first woman to lead a branch of the US Armed Forces, was among those removed by Trump on his first day.