"I take note of the OSCE/ODIHR preliminary findings on the elections which took place yesterday, in the former Yugoslav Republic of Macedonia," he said in a statement.
"I deeply regret the violence which marred the elections" on Sunday, "A day which should have been a peaceful demonstration of democratic values resulted instead in the loss of a life as well as injury to several people," he said.
Rehn quoted the OSCE/ODIHR election observation mission as reporting that that key international standards were not met in the election.
"Organized violence, intimidation and ballot stuffing in many places prevented citizens from exercising their democratic rights. The selective application of the law by the state authorities was also a serious concern," he noted.
Rehn urged the Macedonian authorities to "address these findings and the recommendations which shall follow" and "to duly investigate all reported incidents and bring the perpetrators to justice."
He welcomed Macedonian Prime Minister Nicola Gruevski's commitment to hold a re-run of the election in all the polling stations where there was violence and disorder.
"It is imperative that these re-runs are held in line with international standards," he said, promising that the EU was firmly committed to the European perspective of Macedonia.
He stressed that holding free and fair elections "is an essential part of the political criteria of the EU accession process."
Macedonia's Prime Minister Nikola Gruevski won a landslide victory on Sunday in the country's first early election since the country gained independence in 1991.
The VMRO-DPMNE party led by Gruevski had won 48.13 percent of the votes, far ahead of the Social Democrats' 22.19 percent, with votes from 82 percent of polling stations counted, according to the state electoral commission.
The Democratic Party of Albanians led by Menduh Thaci garnered 10.13 percent, while the ethnic Albanian Democratic Union for Independence got 11.26 percent.
Macedonia, keen to join the EU and NATO, is seeking to launch talks on EU entry and an invitation to join NATO.
Country name dispute with Greece aborted Macedonia's bid to join NATO in April, when NATO invited Croatia and Albania to join in Bucharest, Romania.