The first attacks happened in the neighbouring villages of Birin Bolawa and Birin Fulani in the Nafada district of Gombe, which has been repeatedly targeted by the Islamists.
An election official, who requested anonymity, said: “We could hear the gunmen shouting, ‘Didn’t we warn you about staying away from (the) election?'”
Boko Haram leader Abubakar Shekau said in a video message last month that the militants would disrupt Saturday’s general election, which they see as “un-Islamic”.
The threat and a spate of suicide attacks and bombings against “soft” targets in restive northern Nigeria have prompted the authorities to impose tight security across the country.
The election official said the masked gunmen arrived in Birin Bolawa in a pickup truck at about 8:30 am (0730 GMT), just after accreditation for Saturday’s presidential election had begun.
One voter was shot dead and others fled in panic.
“They set fire to all the election materials we abandoned as we escaped,” he added.
Karim Jauro, a resident of Birin Fulani said the second attack happened at about 9:15 am, adding that had they known about the earlier shooting they would have abandoned the polling station.
“As soon as people saw them they began to run away but the gunmen opened fire on the polling station, killing one man,” he said.
“They burnt the election materials. We strongly believe they are Boko Haram who have been warning people not to participate in the elections.”
Gunmen then stormed the town of Dukku, 80 kilometres (50 miles) from the state capital Gombe city, at about 11:30, shooting randomly as voters queued up at polling stations, residents said.
“They shot dead three people and injured two others,” said Ibrahim Ahmad, adding that the attackers then killed a state assembly lawmaker and the local chief in the nearby herding village of Tilen.
Bala Akilu, another resident who witnessed the shooting in Dukku, supported Ahmad’s account.
“The shooting disrupted accreditation but later some polling stations reopened after the gunmen had left,” he added.
“But others remained shut because voters had gone and were too afraid to return.”