City Comptroller John Liu yesterday rejected a $20 million teacher-recruitment contract sought by the Department of Education, noting it comes even as officials threaten mass layoffs.

Liu said the deal with the staffing and training firm The New Teacher Project was nixed because it was flawed, but he also questioned its timing.

“Twenty million dollars to recruit teachers as the DOE insists on laying off thousands of teachers seems curious at best,” Liu said in a statement.

The city has repeatedly insisted that nearly 4,700 teachers could be laid off this summer.

The DOE said the annual contract cost would be zero if no new teachers are required, but noted there are typically shortage areas that must be filled — including about 400 special-ed positions in the next school year.

“Mr. Liu’s hasty and ill-informed decision completely disregards the needs of thousands of special-education and English-language-learning students, who deserve the best possible teachers we can bring in to our system,” said DOE spokeswoman Natalie Ravitz.