The pair were accused of plotting to topple the government after Iran's election dispute broke out in June, and were allegedly members of the outlawed monarchist group Tondar and Mujahideen Khalq respectively.
Hangings 'to scare people'
Karroubi said the hangings were "to scare people so they do not take part in demonstrations".
"We will by no means allow anything known as the 'green movement' to make an appearance" on the anniversary"
Brigadier General Hossein Hamedani, Revolutionary Guard commander
Mousavi and Karroubi agreed that the executed pair appeared to have been arrested months before the June 12 presidential election and had nothing to do with the post-poll violence.
The hangings were the first reported executions of people tried since a wave of protests that broke out following the re-election of Ahmadinejad to a second four-year term.
Iran's Revolutionary Court began the trial of 16 more people who took part in opposition protests last December on Saturday.
Five of the defendants face charges including "corrupting God's earth" and "waging war against the Islamic goverment".
Hundreds of thousands of Iranians march each year to mark the revolution which toppled the shah, but next month's event is expected to turn into another stage for anti-government protests.
Karroubi's Sahamnews website also said the two leaders had invited people to turn out in "massive numbers" on February 11 for the 31st anniversary of the revolution.
On Saturday, a senior commander of Iran's elite Revolutionary Guards militia warned that any attempt by opposition groups to protest against the government on February 11 would be crushed.
Iranian political analyst defends Tehran's decision to execute Zamani and Rahmanipour
"We will by no means allow anything known as the 'green movement' to make an appearance" on the anniversary, Brigadier General Hossein Hamedani was quoted as saying on ISNA news agency.
He said protesters would be considered as "foreign agents".
"Any voice, colour and gesture which is different from that of the Islamic revolution and from Iranians' voice should be driven out of people's marches ... and if there a few people who want to do something, they will be severely dealt with," he said.
Akbar Hashemi Rafsanjani, the former president and opposition supporter, meanwhile, urged people to maintain calm on the anniversary day.
"Those who love Iran ... should try that this year's march be held calmly ... because any conflict and violence will serve the interests of enemies," Rafsanjani was quoted on state television's website.
The anti-government protests which erupted after president Mahmoud Ahmadinejad's re-election have shaken the pillars of Iran's establishment and divided the clergy.