The government worries that rising numbers are putting strain on education, health and other public services in the country of 86 million, about two thirds of whom are under 35 thanks to a post-war population explosion.
The government first launched a two-child policy in the early 1960s but this was relaxed in a 2003 ordinance that encouraged small families without making it illegal for families to have a third child.
That decree was "so general that people haven't understood it and have sometimes taken advantage of it", said Duong Quoc Trong, deputy head of the government's General Office for Population and Family Planning.
"The demographic boom is damaging the country's sustainable development."
Many of the Vietnamese couples who have a third child do so because they already have two daughters, due to a long-standing belief that sons must care for their parents in old age and carry on the family name.
In the first nine months of the year about 93,000 third-child births were registered in Vietnam, 10 percent more than in the same period last year, according to official statistics released by the office.
This week the cabinet agreed on a draft amendment that would turn the two-child rule into law once it is passed by the National Assembly.
In the past, Communist Party members have faced warnings, reprimands or expulsion for breaching the two-child rule, and citizens have been punished with pay cuts and other disciplinary measures at work.
Officials did not say what penalties may apply in future under the new law.
Some groups will be exempt, including members of ethnic minority groups with less than 10,000 people, said the state-run Vietnam News Agency.
Couples will also be allowed to ask for permission to have a third baby under certain conditions, for example if one of their children is disfigured because of an accident or suffers a fatal disease.
The UN Population Fund's (UNFPA) Tran Thi Van said "Vietnam's population will continue to increase over the next 30 years because of the population momentum, because of the high fertility rate of the past 15-20 years."
However, she told AFP the new third-child birth figures did not match UN data, which had indicated a downward trend in recent years.
The total fertility rate was now below the replacement rate, meaning that, with strict child limits, "it will be difficult to increase the population again decades after," said Van, UNFPA's Vietnam assistant representative.
Van said Vietnam should rethink trying to limit birth rates because "this generation of children will be very important for the country over the 20 years to come in term of development as they will provide the labour force".
"In Vietnam now, life expectancy is rising, the fertility rate is decreasing and in the next 20 years many people will be in the senior group," she said.
"If there is not (a sufficient) labour force as the population is ageing, the country will face a lot of problems."