"I have met with many people and will continue to consider all sides of the issue before making a decision," Richardson said in a statement after the vote.
There are two prisoners currently on death row in the state, but their sentences would not be affected by the repeal.
If Richardson does sign the law New Mexico will become the 15th out of 50 states to end capital punishment in the US.
It would follow New York and New Jersey abolishing the death penalty in 2007 and bills are pending in other states, including Montana and Kansas, to remove it from its statutes.
"The tide is turning across the country, and we are part of that tide," Ruth Hoffman, director of Lutheran Advocacy Ministry and a lobbyist against the death sentence, said.
New Mexico has executed one prisoner, Terry Clark a convicted child murderer, in the past 49 years.
However, more than 1,130 people have been executed nationwide since the US Supreme Court reinstated the death penalty in 1976.