Barnaby Phillips, Al Jazeera's correspondent in Athens, said: "The trade unions here are saying that they succeeded in paralyzing Greece today. Certainly the airports were closed, large parts of public transport were closed and civil servants did not go to work".
Police had deployed more than 15,000 officers in the capital and arrested scores of people ahead of the rally, Panayiotis Stathis, a police spokesman, said.
An appeal by the government to put off the strike, which had been planned weeks in advance of the shooting, was earlier rejected by union leaders.
The killing of Alexandros Grigoropoulos by police on Saturday has touched a raw nerve among young Greeks, angry at years of political scandals and rising levels of poverty and unemployment, worsened by the global economic downturn.
A lawyer for the two officers accused of the killing has said that ballistics show that he was killed by a ricochet and not a direct shot.
Phillips said: "This is potentially good news for the Greek police, but it is coming from the police defence lawyer.
"We haven't heard from the ballistic experts themselves and I think it is going to be very difficult to convince the people on the streets that Alexandros was not deliberately murdered".
One of the officers has been charged with premeditated manslaughter and the illegal use of a weapon and the other as an accomplice. Both have been suspended from duty.
The guard house at the entrance to the courthouse where the two officer were testifying on Wednesday was fire bombed by protesters.
Costas Karamanlis, Greece's prime minister, has vowed to end the country's worst unrest in decades.
He pledged aid packages of $12,000 to stricken businesses, a tax freeze and government-guaranteed loans to restore buildings and property burnt or stolen by looters.
"The government is determined to consolidate the feeling of public safety and to help businesses get back on their feet," he said in a televised national address.
Some newspapers in Greece have put the damage that has taken place across the country at $1.3bn.
Vassilis Krokidis, vice president of the Greek commerce confederation, said: "In Athens, we had 565 shops suffering serious damage or being completely destroyed."
Phillips said: "The prime minister is trying to regain the political initiative but his political opponents are circling, calling for early elections.
"I think the government must be hoping that once today's general strike is over, and if tonight can pass off peacefully, and that's a big if, then maybe the momentum may start to go back in the government's favour but it's early to speculate like that".
A spokesman has denied reports that the government plans to declare martial law.