Police on Saturday had said seven people were killed following the two blasts in Mogadishu, which were claimed by the jihadist Shabaab group.
"The number of victims who were killed in the blasts increased to 20 and more than 40 others have been wounded," said a Somali police official, Ibrahim Mohamed.
He said the toll had risen after some of those wounded on Saturday died in hospital.
Both civilians and members from the security forces were among the casualties, the official said.
Somalia's London-based Universal TV said on Saturday that three of its staff were among the fatalities, naming one as Somali and British dual national Awil Dahir.
Somali President Mohamed Abdullahi Mohamed condemned the "cowardly attacks".
"We will continue defeating terrorists in order to lead the Somali people to stability and prosperity," he said in a statement.
Prime Minister Hassan Ali Khaire visited the wounded in hospital.
The first explosion happened at a checkpoint outside the national theatre, some 500 metres (yards) from the palace on Saturday morning.
The second blast, more powerful according to witnesses, came minutes later at a nearby crossroads.
Mohamed Abdullahi, a senior local official who was slightly wounded in the first blast, said members of his security team were among the dead.
"Seven of my security escort and a driver were among those killed in the blast, but such attacks will encourage our efforts to redouble the war against terrorists", he said in a statement.
A Shabaab statement on Saturday said the Islamist group's "martyrdom operation" had targeted "a security checkpoint that used to protect the presidential palace."
The group was largely driven out of the capital in 2011 and has lost many of its strongholds. But it retains control of large rural swathes of the country and continues to wage a guerrilla war against the authorities.
The group has vowed to topple the internationally-backed government.
The worst carnage to date in Somalia occurred on October 14 last year when 512 people were killed in Hodan, a busy commercial district in the capital. (AFP)