Which two prophets urged the Jews to resume building the temple?

Answer: Haggai and Zechariah

Haggai and Zechariah son of Iddo prophesied, and the elders built and prospered through their prophesying.

“Later, the prophets Haggai and Zechariah son of Iddo prophesied to the Jews in Judah and Jerusalem in the name of the God of Israel, who was over them.”— Ezra 5:1 (BSB)