"The Action and Solidarity party faction supports and will ensure the formation of a new government that will focus on security and economic development," Grosu said on social media.
The official thanked Gavrilita for her dedication and efforts as prime minister.
Earlier in the day, Moldovan Prime Minister Natalia Gavrilita announced her resignation.
"After a year and a half at the head of this government, it is time to announce my resignation from this position," Gavrilita told reporters.
The government of Moldova enjoyed support from international partners, but did not see similar support from the country's population, she added.