Sessions wrote that his decision comes in light of last week’s testimony by fired FBI Director James Comey.
State lawmakers will return to work on their budget negotiations next week.
Trump says that he never asked Comey for a pledge of loyalty.
House Republicans on Thursday upheld a ruling by Speaker Tim Moore that the “extra session” was unnecessary and invalid.
It passed its final of three votes in the House 64-51.
Comey accused the Trump administration of spreading “lies, plain and simple.”
The bill would require two successful supervised visits before recommending children go back to their parents.
The House voted 65-54 Wednesday to tentatively approve the bill.
The proposed session would begin Thursday and continue for 14 days.
Comey is set to testify before the Senate Intelligence committee Thursday. His prepared statement was released Wednesday afternoon.