The chairman of the House Democrats' campaign operation has joined those calling for Veterans Affairs Secretary Eric ShinsekiEric ShinsekiShulkin confirmed to lead Dept. of Veterans Affairs Dems to Trump: Exclude VA from hiring freeze Dems, GOP battle over pace of Trump confirmations MORE to resign.

Rep. Steve Israel (D-N.Y.) is the first member of the House Democratic leadership team to call for Shinseki's head.

He told CNN that Shinseki's resignation won't solve the problems at the VA, but that he should still be dismissed.

"He should resign, in my view," said Israel, the chairman of the Democratic Congressional Campaign Committee. "But there are too many of my colleagues saying that that resignation is going to solve the problem. It's not going to solve the problem. What is going to solve the problem is a criminal investigation, with or without his resignation."

A number of vulnerable House and Senate Democrats have called for Shinseki to resign, raising the pressure on the White House. 

But Democratic leaders have refrained from the calls. Israel's remarks came hours after House Minority Leader Nancy Pelosi (D-Calif.) said she didn't think Shinseki should resign.

Israel reiterated his position in a statement to The Hill.

"If it will help fix the problem to clean house, then yes, he should resign, but my main concern is getting to the root of the problem here, and I want to make sure any steps taken actually lead to drastic improvements for our veterans," he said.