Partizan, who were 11 points clear at the top a month ago, saw their advantage over bitter city foes Red Star slashed to only two points after they were held to a 0-0 draw at Novi Pazar on Sunday.
Belgrade's big two meet in a crunch and potentially explosive derby on May 18 and Rasovic was confident Partizan would win a record sixth successive league title.
"You can't choose when you are going to take over at a club like Partizan but you have to be ready and I am certainly ready, although it's a delicate situation," Rasovic told a news conference at the club's stadium.
"We are good enough to preserve our lead in the last five games and it's now imperative to win our next match at home to Radnicki Nis.
"I've been here a long time as an assistant, I know the players well and I am sure they have it in them to get going again. Many people might have been reluctant to step up under these circumstances but I really relish the challenge."
Vermezovic's departure came after the club's sports director Ljubisa Tumbakovic quit last week to take over as manager at Chinese first division side Wuhan Zall following a rift with Partizan's president Dragan Djuric.
"We are sad to have parted company with Vermezovic but sometimes hard work doesn't yield results and in football only the results matter at the end of the day," said Djuric.
"We will sit down with Rasovic in a few days to determine the length of his contract and hammer out all the details."