The earlier attack in Farah province killed at least 16 and injured 20
A controversial former Afghan warlord has narrowly escaped an assassination attempt which killed at least five of his bodyguards, police say.
Abdul Rasul Sayyaf, now an MP, was travelling north of Kabul when a remote-controlled bomb hit his convoy.
It is not clear who attacked Mr Sayaf, an ally of President Hamid Karzai, who was sworn in on Tuesday for a second term after controversial elections.
Earlier at least 16 people were killed in a suicide bomb in the south-west.
Mr Sayyaf was attacked in Paghman district, north of Kabul.
Mr Sayyaf, an ethnic Pashtun former warlord allied to the president, supported the anti-Taliban Northern Alliance between 1996 and 2001, when the Taliban were ousted, and became an MP in 2005.
Human Rights Watch have accused him of war crimes.
Western leaders are putting pressure on Mr Karzai to deal with corruption and remove former warlords from his government.
Motorcycle bomber
The earlier attack, in a crowded market in Farah city, capital of Farah province, killed at least 16 people and wounded more than 20, police said. A policeman was among the dead.
Farah, a mainly desert province on the Iran border, has seen a rise in insurgent attacks this year as the Taliban have become active in new areas.
The suicide bomber on a motorcycle struck in an area where heavy trucks were being loaded with goods to be taken to the province of Herat, police said.
Several dozen people, mostly civilians, were wounded in the attack, officials said.
More than a dozen were critically injured so "the death toll may rise", provincial governor Rohul Amin told Agence France-Presse news agency.
"The bomber riding on a motorcycle detonated himself at a main square near my working office, in my home," the governor said.
The blast damaged some nearby buildings, he added.
The two attacks come a day after President Karzai took over for a second term, promising to work towards building a secure and stable Afghanistan.
Kabul, AfghanistanAfghan police have said that a member of parliament (MP) escaped an assassination attempt on Friday night near the capital of Kabul. Five bodyguards, however, died.

An Afghan district police chief told the Voice of America news agency that a remote-controlled bomb targeted the convoy of Abdul Rab Rasoul Sayyaf as it moved along roads outside the capital. It was not immediately clear who was responsible for the attack.

Sayyaf is an MP from the Kabul province, and a former warlord. This was not the first attempt on his life; he has survived at least one other similar attack.

Sayyaf was one of the ex-mujahideen leaders who fought against the Taliban in the mid-1990s.  He became a strong supporter of Afghan President Hamid Karzai's government and the international forces after the United States-led invasion in 2001. The Human Rights Watch, however, has accused him of war crimes.