Social Services Minister Paula Bennett and Transport Minister Simon Bridges said they were both running to become deputy leader and would back English's leadership bid.
Mr English, who is also deputy leader of the ruling centre-right National Party, announced his candidacy on Tuesday after Mr Key's resignation statement on Monday.
Health Minister Jonathan Coleman and Police Minister Judith Collins have also put their names forward.
Other contenders, such as senior cabinet minister Stephen Joyce, may yet still emerge before the party holds a caucus meeting on Monday to vote for a new leader.
"Bill does look in a very strong position to take this," said Jon Johansson, political scientist at Victoria University in Wellington.
Several cabinet members, including Immigration Minister Michael Woodhouse and Primary Industry Minister Nathan Guy, have declared their support for Mr English.
A recent UMR survey of voters pegged Mr English as favourite to replace Key on 21%, followed by Mr Joyce on 16%, Ms Bennett on 11% and Ms Collins on 6%. Mr Coleman was not ranked in the survey, which was conducted in early October, but said he had youth and energy on his side.
National elections are not expected until late 2017.
Mr Key has been New Zealand's leader since 2008 and the National Party is part way through a third, three-year term that has been marked by political stability and economic reform.
Some questioned whether the clamour over the leadership contest pointed to more turbulent times for the National Party.
New Zealand First Leader Winston Peters, with whom the National Party may need to strike a deal to form a parliamentary majority after the 2017 election, traded jabs with Mr Key on Wednesday in parliament.
"All we're hearing from ... the spills coming out of caucus is terrible instability, feuding, backstabbing, fighting," Mr Peters said.
Mr Key laughed off the attack, pointing towards opposition parties and saying: "We actually have a capable caucus in which we actually know each other and like each other, quite a bit different from over there."
