The deadly attacks, in which suicide bombers blew themselves up in vehicles, targeted two towns in Hama province that are majority Alawite, the religious community to which President Bashar al-Assad belongs.
The first bombing, in the town of Jibrin, in the southwest of the province, killed 17 civilians, including the 11 children, state media said.
The second attack hit the town of Al-Humairi and killed one person, state news agency SANA reported.
The Britain-based Syrian Observatory for Human Rights said at least 15 people had been killed in the attacks.
They come after a double car bombing claimed by Al-Qaeda's Syria affiliate Al-Nusra Front killed at least 100 people on Tuesday in a majority Alawite district of the central city of Homs.
This week also saw 33 civilians killed in the main northern city of Aleppo on Thursday when government aircraft bombed a popular market in a rebel-held district.
Despite the violence, Syria's government plans to hold the country's first multi-candidate presidential elections in just over a month's time on June 3.
Assad is widely expected to sweep to victory in the vote, the first since a constitutional amendment did away with an old system of presidential referendums.
But 23 other hopefuls have also submitted applications to stand, although only Assad and a maximum of two other candidates are expected to secure sufficient backing in parliament to get their names on the ballot.
The Supreme Constitutional Court is expected to announce which candidates have made the cut on May 6.
The government has not explained how it will organise countrywide elections with violence that has killed more than 150,000 people ravaging much of Syria.
Large swathes of the country are beyond government control and the violence has forced nearly half Syria's citizens to flee their homes.
The conflict in Syria began in March 2011, with peaceful anti-government protests that the regime tried to put down with force.
Much of the opposition took up arms and the country has since sunk into a civil war that has proved impervious to international mediation efforts.
Since early January, moderate and Islamist rebels, along with Al-Nusra Front, have also been battling against the jihadist Islamic State of Iraq and the Levant (ISIL).
The group has gained notoriety for abuses against both civilians and rival opposition fighters.
ISIL has its roots in Al-Qaeda's Iraq arm, but has since fallen out with the organisation, whose chief Ayman al-Zawahiri has regularly called on it to leave Syria and focus on Iraq.
In a new audio recording posted online Friday, Zawahiri for the first time ordered Al-Nusra's chief Mohammed al-Jolani to end fighting with ISIL.
Zawahiri ordered that "all soldiers of the Front immediately cease fighting" other jihadist groups.
Instead, he urged Jolani to "devote himself to combat the enemies of Islam, specifically Baathists, Shiites and their allies."
The Baath is Syria's ruling party, which is headed by Assad.
Zawahiri also repeated his call for ISIL to leave Syria, urging the group's chief Abu Bakr al-Baghdadi to "devote himself to wounded Iraq, which needs you to redouble your efforts" there.
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Damascus (AFP) - Eleven children were among 18 people killed in two bombings in central Syria Friday, state media reported, as Al-Qaeda's chief called on its Syrian
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Children among 18 dead in two Syria bombings
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11 children among 18 dead in car bombings in Syria's Hama: state TV: May 02, 2014 10:59 AM (Last updated: May 02, 2014 01:47 PM)
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Suicide bombers blew up two vehicles in the central Syrian province of Hama on Friday, killing at least 18 people, including 11 children, state media reported.
11 children among 18 dead in Syria car bombings ...
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Damascus. Suicide bombers blew up two vehicles in central Syria on Friday, killing at least 18 people, including 11 children, state media reported, cited by AFP.
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11 children among 18 dead in Syria car bombings: state media. AFP , Friday 2 May 2014. Print. Send. Tweet.
11 children among 18 dead in Syria car bombings: state ...
DAMASCUS, May 2, 2014 (AFP) - Suicide bombers blew up two vehicles in central Syria on Friday, killing at least 18 people, including 11 children, state media reported
