WASHINGTON — Pushing back against the accelerating criminal investigation into his campaign’s ties to Russia, President Trump argued on Sunday that its focus should instead be on his 2016 rival, Hillary Clinton, even as the special counsel’s inquiry was reportedly poised to produce its first indictment.

In a series of tweets, Mr. Trump said Republicans were now fighting the Russia allegations by looking into Mrs. Clinton, apparently referring to new House investigations into her email practices and an Obama-era uranium deal with Russia. But the president made it clear he believed that Mrs. Clinton should be pursued more forcefully, writing, “DO SOMETHING!”

He did not say who should take action or what it should be, though critics have accused him of trying to sway the congressional and special counsel inquiries into Russian ties. Still, the outburst suggested that Mr. Trump, increasingly angry and frustrated about the investigations, is waging a concerted campaign to shift the focus to Mrs. Clinton and other Democrats.

After long expressing anger that his allies have not done enough to protect him from the inquiries, he is now enlisting White House and administration officials, employing his vast social media presence, and putting pressure on the Republican-led Congress to deflect any potentially damaging reports.