Kagan issued an order effectively putting the litigation on hold and preventing enforcement of the subpoena pending a further order by her or the full court.
Kagan is the justice designated to handle emergency appeals from a group of states including Arizona.
The panel sought the records as part of its investigation into events surrounding the deadly Jan. 6, 2021, assault on the Capitol by Trump supporters who sought to block Congress from certifying his election loss to Democrat Joe Biden.
Trump, who is considering another run for the presidency in 2024, has accused the panel of waging unfair political attacks on him.
The panel had already been in the process of seeking records concerning Ward, who the panel said participated in multiple aspects of the attempts to interfere with the electoral count.