(Adds Helmand attack)
KABUL, June 2 (Reuters) - Three Turkish construction workers were killed on Monday when a suicide bomber blew himself up near a police building in east Afghanistan and three policemen were killed in an attack in the south, officials said.
The Taliban summer offensive, launched in mid-May, is ramping up ahead of the second round of voting in the presidential elections on June 14.
In the final week of May, Western security sources recorded a 10 percent rise in attacks around the country and expect numbers to increase as the vote approaches.
In the eastern province of Nangarhar, a suicide bomber killed three Turks and injured two other people including a child, police said.
"Turkish engineers were entering the facility by car when the rickshaw loaded with explosives blew up," said provincial police chief Fazel Ahmad Shirzad.
The Taliban did not immediately claim responsibility but said it was looking into the incident.
In southern Helmand province, a district governor said his compound was attacked by Taliban suicide bombers and gunmen. The Taliban confirmed they had carried out the attack.
"Three Taliban armed with light and heavy weapons attacked our offices in Greshk city this morning," said Greshk district governor Mohammad Akbar.
"As a result, three policemen were killed and three were wounded." (Reporting by Mirwais Harooni in Kabul and Mohammad Stanekzai in Lashkar Gah; Writing by Jessica Donati; Editing by Nick Macfie)