General Ali Fadavi accused those detained of "unprofessional" acts.
But he suggested the group, who are being held by the guards, could be released soon.
The incident comes at a sensitive time, as the US and Iran try to implement the deal on Iran's nuclear activities.
US Secretary of State John Kerry has contacted Iranian Foreign Minister Javad Zarif over the incident.
Giving his assessment of the talks, Gen Fadavi said "Mr Zarif had a firm stance, saying that they were in our territorial waters and should not have been, and saying that they [the US] should apologise".
"This has been done and it will not take long, and the naval force, according to its hierarchy, will act immediately upon the orders it receives," he added.
This naval incident comes at a delicate moment for both Washington and Tehran.
The process to begin lifting the sanctions imposed on Iran due to its nuclear activities is expected to get under way at the end of this week.
There are many conservatives and hardliners in both countries who would dearly love to sabotage the deal and consequently both governments may be eager - whatever the attendant rhetoric -  to get this episode resolved as quickly as possible.
How it plays out will be an important signal as to the balance of power in Tehran itself.
The Revolutionary Guard Corps, whose naval branch detained the US vessels and their crews,  is amongst the more hardline elements ranked up against the nuclear deal.
But the potential economic benefits of lifting the sanctions may be too great an inducement for the agreement to be derailed now.
US officials have said the sailors - nine men and a woman - are likely to be released on Wednesday. There has been no confirmation from Washington that Mr Kerry apologised.
One of the two US riverine patrol boats developed mechanical problems while on a training mission between Bahrain and Kuwait, the US officials added.
The crew and vessels have been taken to Farsi Island, the site of an Iranian naval base.
Iran's influential Revolutionary Guard - tasked with protecting the country's 1979 Islamic revolution - has strongly defended Iranian sea borders in the past.
Fifteen British sailors and marines were held for 13 days in 2007 after they were captured in a disputed area between Iran and Iraq.
Despite last year's breakthrough nuclear deal tensions remain between the US and Iran.
In December, Iran's navy conducted rocket tests near US warships in the Strait of Hormuz, something the US called "highly provocative".

Trevor Wright, 67, of Ballingdon Street, Sudbury, was found guilty at Ipswich Crown Court of five charges of rape and seven of sexual assault.
He had already admitted six more sex assaults on the same three victims.
Judge Martyn Levett granted Wright conditional bail and told him he would be sentenced later this month.
One rape took place in a car belonging to a customer at Wright's garage in Ballingdon Street, the court heard.
Other offences took place at a stables where Wright kept a horse.
One sex assault was in a swimming pool in Devon while Wright was on holiday, prosecutor Andrew Thompson said.
Wright said although he was "sex obsessed", he denied the further assaults or committing rape.
He had told police he had been a heavy drinker and suffered from memory problems.

Four men, aged 17, 18, 25 and 27, were injured during the incident, which took place in Whatriggs Road in the early hours of Saturday.
They were taken to the town's Crosshouse Hospital for treatment and were later released.
Police said four men, aged 17, 18, 19 and 20, had been arrested in connection with the incident.
They are expected to appear at Kilmarnock Sheriff Court on Monday.
The US has apologised to Iran after 10 American sailors were arrested for entering Iranian waters, the commander of Iran's Revolutionary Guards naval forces has said.
[NEXT_CONCEPT]
A garage owner who preyed on three schoolgirls between 1977 and 1989 has been convicted of rape and sexual assault.
[NEXT_CONCEPT]
Four men have been arrested after four people were stabbed during a disturbance in a Kilmarnock street.