In one incident on Monday 20 were reported killed and another 20 injured in a blast in the town of Spin Boldak, close to the border with Pakistan.
The Pakistan-based Afghan Islamic Press news agency quoted a spokesman for the ousted Taliban government as claiming responsibility for the blast, which he said was a caused by a remotely controlled bomb.
Also on Monday a separate blast in the main town of Kandahar killed three Afghan soldiers as well as the bomber and injured several civilians.
The blasts come just a day after another suicide attack claimed the life of a Canadian diplomat and two Afghan soldiers.
Two Canadian soldiers based in Kandahar - a former Taliban stronghold - were also injured in the attack.
News of the latest attacks came just hours after Hamid Karzai, the Afghan president, expressed his concern at the increasing use of suicide tactics by the Taliban insurgents.
Speaking to journalists inside his heavily fortified palace, Karzai said the increased use of suicide attacks was a sign of Taliban desperation.
A witness in Kandahar who gave his name only as Assadullah said the bomber in the suicide attack appeared to be a teenager.
"I saw a boy of about 15 with an explosives' vest running towards the car and then heard the explosion from across the street," he said. "I ran for cover and saw the casualties when I got up."
Taliban fighters have carried out a series of suicide attacks, mainly targeting US-led troops and Nato peacekeepers, in the past few months, but they have not caused major casualties among foreign forces.
Security analysts suspect the Taliban has stepped up suicide attacks after seeing al-Qaida's success in Iraq.
The attacks have come at a time when America's Nato allies are planning to take over more responsibility from US troops in Afghanistan, and Washington is looking to scale down its commitment.
Karzai said he had intelligence reports some months ago that suicide attackers were being trained in frontier areas and most attacks were carried out by "foreigners".
Despite the threat posed by suicide bombings, on Karzai's orders police have begun removing some checkpoints and security barriers set up around Western installations in the capital Kabul, in order to ease traffic congestion.