Christian Tybring-Gjedde, an MP, and former justice minister Per-Willy Amundsen said Mr Trump “had taken a huge and important step in the direction of the disarmament, peace and reconciliation between North and South Korea”.
Both men are politicians with the anti-establishment Progress Party.
A group of US Republican politicians nominated Mr Trump for the prize in May.
The process of considering candidates for the honour is carried out in Norway, and nominations must be sent to the Nobel committee before February.
Mr Trump’s recent backing from Norwegian and US politicians therefore serve as nominations for the 2019 prize.
Each year the winner is announced on the Friday of the first full week of October.
The committee cannot publicly reveal who has been nominated, so it is unclear if Mr Trump is in the running to scoop the prize in 2018.
Mr Trump’s Norwegian nominations come after UK bookmakers slashed the odds of him winning after his summit with Kim Jong Un in Singapore.
Sky Bet is offering odds of the US president winning the award this year at 8/1, while it puts the chances of him winning the prize alongside someone else at 5/4.
Mr Trump and Mr Kim pledged to work towards the complete denuclearisation of the Korea peninsula at the summit on the resort island of Sentosa.
US secretary of state Mike Pompeo admitted there was still “a lot of work left to do”, with the US wanting to see “major disarmament” of North Korea within two and a half years.
Mr Pompeo has also said sanctions on North Korea will not be eased until the country has denuclearised.
The UK foreign secretary Boris Johnson said in May that Donald Trump deserves to be in the running for the honour if he can “fix” North Korea and the Iran nuclear deal.
The foreign secretary, who was speaking on a trip to Washington DC, said: “If he can fix North Korea, and he can fix the Iran nuclear deal, then I don’t see why he’s any less of a candidate for the Nobel Peace Prize than Barack Obama, who got it before he even did anything.”
Mr Obama was awarded the prize in 2009 less than a year after entering office.
Mr Trump has been tipped for the award as he celebrates his 72nd birthday on Thursday.
He was the second oldest person to assume the US presidency when he took office in 2017. Ronald Reagan was 73 when he was re-elected in 1984.