"My role is over," a ministry official quoted Cho as saying. He also apologized for "causing trouble" to the people and the president.
Cho has been under pressure to quit since a confrontation between the South Korean and North Korea navies two weeks ago in the Yellow Sea.
A South Korean ship fired warning shots at a North Korean vessel and then the navy filed a misleading report on the incident, according to officials.
A top general was sacked on Monday after admitting to leaking information to the press about the incident.
"Sooner or later, I will deliver my intention (to the presidential office) to step down as defense minister," Cho said, according to the ministry.
He said he wanted to leave the military in a "duly responsible" manner.
President Roh Moo-Hyun would decide whether to accept Cho's resignation "by no later than Thursday," his spokesman Kim Jong-Min told journalists.
On July 14, South Korean navy ships fired warning shots to drive away a North Korean patrol boat that had intruded into southern waters in the Yellow Sea.
The initial report on the incident omitted to note ship-to-ship radio contact had taken place at the time of the confrontation.
Five senior military officers were reprimanded for filing the incomplete report, and on Monday one of them, Lieutenant General Park Sung-Choon, was fired from his job as head of the defense intelligence agency for the Joint Chiefs of Staff.
Park was dismissed for disclosing to the media the contents of the radio exchanges, which showed North Korea had sought to mislead the South Korean navy by claiming the intruding North Korean navy vessel was a Chinese fishing boat.
Park reportedly said he had leaked the information in order to justify the South Korean navy's handling of the confrontation, including the decision to fire warning shots.
The navies of South and North Korea agreed last month to open radio contact for the first time in an effort to reduce tension and the chance of confrontation along the disputed maritime border in the Yellow Sea, scene of fatal clashes in the past.
Last week, a special defense ministry investigation said South Korean navy officials made "a mistake" by judging that the "deceiving" North Korean radio messages did not merit reporting.
But Defense Minister Cho on Saturday told parliament his naval officers deliberately omitted to mention the radio contact out of concern that if they did so, higher authorities might over-rule plans to use force against the North Korean boat.
Cho, 64, joined the army in 1962, served in the Vietnam War as a company commander and rose to be commanding general and chairman of the Joint Chiefs of Staff.
He was made defense minister in February 2003.