Iraqi government spokesman Ali al-Dabbagh said the bombs "represent an extension" of activities by insurgents linked to Saddam Hussein's regime, Associated Press news agency reported.
But he stopped short of directly connecting the blast with the hanging of Majid.
The man known as Chemical Ali had received several death sentences, including for the mass killing of Iraqi Kurds in the village of Halabja in 1988.
The BBC's Jim Muir in Baghdad says it is clear Monday's bombs were co-ordinated and intended to undermine recent security gains as Iraq prepares for a March general election.
The first explosion toppled large concrete blast-walls like dominoes outside the Sheraton, by the Tigris River, causing a huge cloud of dust to envelop the hotel.
Ceiling collapses
An Iraqi journalist, Zina Tareq, who was in her office at the time, told how she dived under a desk with the five-year-old daughter of a colleague.
The blasts come six weeks before parliamentary elections
"We heard a deafening sound. The ceiling collapsed on us and the windows shattered," she told Reuters news agency.
The second and third bombs went off within minutes near the Babylon Hotel in the central district of Karrada, and close to the Hamra Hotel in the southern district of Jadriyah.
The Iraqi military spokesman in Baghdad, Maj Gen Qassim Atta, said all three attacks were suicide car bombs, reports AFP news agency.
The blasts differed from others recently in that they appeared to target hotels rather than government buildings.
Attacks in August, October and December last year - which killed nearly 400 people - rocked the ministries of finance, foreign affairs and justice.
DEADLIEST ATTACKS SINCE 2003
Mar 2004: 171 killed in bombings in Baghdad and Karbala
Nov 2006: 202 killed in multiple blasts in Baghdad
Mar 2007: 152 killed in truck bombing in Talafar
Apr 2007: 191 killed in car bombings in Baghdad
Aug 2007: More than 500 killed in attacks on villages near Sinjar
Aug 2009: 95 killed in lorry bombs in Baghdad
Oct 2009: 155 killed in twin truck bomb attacks in Baghdad
Dec 2009: At least 127 killed in a series of car bombs in Baghdad
Source: News agencies, BBC
Iraqi Prime Minister Nouri Maliki blamed the bombs in August and October on groups loyal to Saddam Hussein's now-banned Baath Party.
There have been fears of more violence ahead of the 7 March election, seen as important for consolidating Iraq's democracy and keeping a US military exit by the end of 2011 on schedule.
Our correspondent says the latest attacks come against a background of generally improved security in the country.
But insurgents are clearly bent on trying to shake stability before the election, he adds.
It is to be the second parliamentary ballot since the 2003 US-led invasion that ousted Saddam Hussein.
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