The Democrat also said he's not getting involved in who should lead the State Assembly, despite a published report that suggested otherwise.
Assembly Speaker Sheldon Silver (D-Manhattan) declined to comment.
Cuomo said federal charges that a state senator tried to bribe political leaders to get a spot on the New York City mayoral ballot and another case involving an assemblyman selling legislation to protect business associates has created a political opportunity to change the state's weak election laws.
"You can make major reforms when you have the people's attention, and we have the people's attention, and I think that's a good thing," Cuomo said on a local public radio program. "I've been waiting for this moment for many, many years."
Cuomo said he wants to look at tightening campaign-finance laws, strengthening the ability of boards of elections and prosecutors to go after wrongdoing, and eliminating the practice of allowing a political party to give its ballot line to someone from another party.
The governor didn't spell out exactly the changes he wants. But he said the "crisis" shouldn't be wasted.
"I think we should now take this time and pull back the lens and broaden our reform mandate that we consider in this session," he said.
Seeking perhaps to distance himself from the arrests, Cuomo said the controversies were a New York City problem more than an Albany concern. He added that no law could stop all political corruption.
Last week, federal prosecutors accused state Sen. Malcolm Smith (D-Hollis), a Republican New York City councilman, two Republican county leaders and two others of involvement in a bribery scheme to get Smith a spot in the GOP mayoral primary this fall.
Two days later, federal authorities charged Assemb. Eric Stevenson (D-Bronx) with taking bribes and offering to write legislation to protect certain owners of adult day care homes from competition. In that case, Assemb. Nelson Castro (D-Bronx) gathered information for prosecutors and resigned his office to settle unrelated charges.
After presenting both cases, Manhattan U.S. Attorney Preet Bharara said political corruption was "pervasive" in the state and added that the "show-me-the-money culture in Albany is alive and well."
Groups that support public financing of political campaigns have tried to seize the moment to say now is the time to get money out of politics.
Others, including Citizens Union, said more is needed than campaign-finance changes -- including allowing open primaries that allow multiple candidates from one party. They said that would eliminate "party bossism" that controls the ballot.
Citizens Union also said the attorney general's office should be given power to investigate election-law violations and audit "member items," or lawmakers' pet projects.
Cuomo, a former attorney general, called for similar changes in 2010, but he omitted them from his list Monday.
A New York Post story Monday said Cuomo was looking to use the scandals as a way to oust Silver, who has led the Democrat-dominated chamber for 20 years. While not addressing Silver directly, the governor said he wasn't going to get involved in leadership decisions.
"It is wholly up to legislative bodies to select a leader," Cuomo said. "I would never, even for a moment, try to influence that decision."