At least three people were killed and 38 wounded in the carnage, which underscores rising insecurity in Afghanistan from the resurgent Taliban.
A suicide car bomber struck an Afghan police precinct in western Kabul and a gunbattle ensued, the interior ministry said, in a continuing attack which sent clouds of acrid smoke billowing into the sky.
Five minutes later a suicide bomber blew himself up at the gates of an Afghan intelligence agency branch in eastern Kabul as another attacker was gunned down while trying to enter the compound, the ministry added.
The Taliban claimed both assaults, with spokesman Zabihullah Mujahid calling them "martyrdom attacks" in a Twitter message.
The health ministry said the wounded, some of them in critical condition, had been rushed to hospitals.
"More casualties are expected as the ambulances are on their way," ministry spokesman Waheed Majroh told AFP.
Afghan police and troops are battling a resurgent Taliban as the insurgents escalate nationwide attacks, even in winter months when the fighting usually wanes.
The latest violence comes two days after an Afghan policeman linked to the Taliban shot dead 11 of his colleagues at a checkpoint in the southern province of Helmand, in the latest so-called insider attack.
Such attacks -- when Afghan soldiers and police turn their guns on their colleagues or on international troops -- have sapped morale and caused deep mistrust within security ranks.
Afghan forces, beset by record casualties, desertions and non-existent "ghost soldiers" on the payrolls, have been struggling to rein in the Taliban since US-led NATO troops ended their combat mission in December 2014.
Extra troops were needed to end the stalemate in the war, Nicholson, the top US commander in Afghanistan, told the US Congress in what could be President Donald Trump's first major test of military strategy.
Separately, the Pentagon this year said it would deploy some 300 US Marines this spring to Helmand province alone.
The Marines will assist a NATO-led mission to train Afghan forces, in the latest sign that foreign forces are increasingly being drawn back into the worsening conflict.
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