Daines visited Jerusalem as concern was high among officials that Iran was purposely inflaming tensions in the West Bank to distract Israel from its pursuit of a nuclear weapons program.
Michigan State Senator Sylvia Santana said that she "should have exercised better discretion" before going on the trip.
McConnell, who has served in the Senate since 1985, fell and suffered a concussion and a broken rib in early March and missed six weeks of Senate action.
The issue has been in the national spotlight with the arrest last month of Jack Teixeira, a 21-year-old low-ranking member of the Air National Guard accused of taking advantage of his clearance.
The request was made by Democratic Senator Chris Van Hollen in a letter sent to US Secretary of State Antony Blinken on Tuesday.
Among the senators who joined the call were Ben Cardin (D-MD), Chris Murphy (D-CT), Tim Kaine (D-VA), and Cory Booker (D-NJ).
The lawmakers accused the Biden administration of allowing "taxpayer-funded antisemitism" at colleges and universities across the country.
Called the FDA Modernization Act 2.0, the bill, signed into law by US President Joe Biden, saw support from Republicans and Democrats alike.