Analysts say Mr Hu's visit is the most important by a Chinese leader in 30 years given China's growing military, economic and diplomatic clout.
Relations have been strained on issues from currency controls and trade disputes to human rights and Taiwan.
Talks are also expected to include North Korea's nuclear activities.
Mr Hu stepped off a jet plane to a show of pomp at Andrews Air Force base outside Washington on Tuesday, greeted by US Vice-President Joseph Biden.
In the US capital, meanwhile, raucous demonstrators protesting against China's Tibet policies gathered in front of the White House, waving signs and flags and chanting slogans.
Workers hung US and Chinese flags along Pennsylvania Avenue, one of Washington DC's chief arteries, which runs between the White House and the Capitol building where Congress sits.
Tuesday's dinner will be followed on Wednesday by talks in the Oval Office, during which White House aides pledged the US president would engage his counterpart on the top issues facing the two nations.
Hu Jintao's Itinerary
- 18 Jan: Arrives in Washington, has private dinner with US President Barack Obama
- 19 Jan: Series of bilateral meetings followed by joint press conference; lunch with Vice-President Joe Biden; formal state dinner
- 20 Jan: Visits Capitol Hill to meet congressional leaders; departs for Chicago
- 21 Jan: Leaves Chicago for Beijing
"Whether we're dealing with economic discussions, whether we're dealing with those in the security realm, or whether we're doing those with human rights, I think this is an argument that we have and we'll continue to make to the Chinese and push them to do better," spokesman Robert Gibbs told reporters.
On Wednesday evening Mr Obama will host an opulent state dinner.
Later in the week, Mr Hu is expected to travel to Chicago, where some predict he will sign a series of trade and investment agreements.
China's foreign ministry called Mr Hu's visit "an important one".
"We hope the visit will promote positive and co-operative China-US relations, map out new directions for bilateral relations in the new era and raise co-operation to a new level," said spokesman Hong Lei.
“Start Quote
End Quote Damian GrammaticasThere are countless ways of characterising the relationship between these two nations, but almost every one is animated by the idea that we are witnessing an historic shift”
This is likely to be Mr Hu's last state visit to the US before a handover of power is completed in China in 2013.
US Secretary of State Hillary Clinton has said that America and China are "at a critical juncture, a time when the choices we make, big and small, will shape the trajectory of this relationship".
Both sides recognise the deep divisions that have dogged relations over the past year: the value of the yuan, the huge trade gap, human rights, US arms sales to Taiwan.
The US is also concerned by China's growing military strength.
Earlier this month, during a trip to China by US Defence Secretary Robert Gates, Beijing confirmed that it had tested a prototype J-20 stealth fighter, invisible to radar.
The US has also bolstered its support for its East Asian allies, most notably South Korea and Japan amid maritime rivalries with China in the Pacific.
The two powers have also been at loggerheads over how to curb North Korea's belligerent behaviour and advancement of its nuclear programme.
In a rare interview with foreign media, Mr Hu acknowledged the "differences and sensitive issues", but said co-operation rather than confrontation would serve both sides best.
'Manipulation'Ahead of Mr Hu's arrival in the US, a Chinese trade mission signed six deals with US companies in Houston worth $600m (£376m) - which analysts say is an attempt to create a "positive" atmosphere for the talks.
“Start Quote
End Quote Joseph Nye Professor at Harvard UniversityThe relationship will remain difficult as long as the Chinese suffer from hubris based on a mistaken belief in American decline”
Trade between the US and China is worth $400bn, up from $100m 30 years ago, when the US formalised relations with the communist state.
The US is also encouraging China to buy tens of billions of dollars of aircraft from Boeing, car parts, agricultural goods and beef.
A series of deals on bilateral trade, energy, environmental protection, infrastructure building, and cultural exchanges are expected to be signed during the visit, Chinese state media reported.
Meanwhile, US senators have been pressing Congress to penalise Beijing for "manipulating" its currency.
They say it is important to punish China if it does not allow the yuan to rise in value rather than manage its exchange rate - making Chinese products cheaper in the US and raising the price of US goods in China.
Mr Hu earlier said the yuan was not undervalued, and that China had adopted a "managed floating exchange rate regime" determined by the balance of international payments and supply and demand.
He also questioned the role of the US dollar as the world's reserve currency and criticised US monetary policy, saying that by keeping interest rates low, the Federal Reserve was devaluing the dollar and creating inflation elsewhere.
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