Nearly a week after Donald Trump rejigged his faltering presidential campaign, rival Hillary Clinton still holds her lead but the gap has gradually eroded to six points compared to the 13-point lead early this month.

Clinton, the Democratic nominee, has the support of 48 per cent of registered voters while Republican Trump is favoured by 42 per cent, according to the NBC News/Survey Monkey weekly election tracking poll released on Tuesday.

Last week Clinton led Trump by eight percentage points and in early August she had a 13-point lead over the tycoon with likely voters and 12 points ahead with all registered voters.

In some polls, Clinton leads Trump by 10 percentage points immediately after two back-to-back conventions. But the margin gradually has narrowed in the past one week.

On August 18, Trump rejigged his campaign for the second time in two months following poor showing in the polls. He inducted fresh faces to propel his faltering presidential bid.

The 70-year-old controversial Republican nominee hired Stephen Bannon, the executive chairman of the conservative website Breitbart News, as CEO of his campaign and promoted one of his advisers – Kellyanne Conway – as campaign manager.

His campaign said the new appointments were designed to bolster "business-like approach" of Trump’s campaign.

In the Monmouth University poll conducted last Thursday through Sunday, Clinton was leading Trump by seven points.

A new poll released by Three Emerson College showed that Clinton and Trump each have 43 per cent support in Ohio.

In Michigan, Clinton led Trump by five points, 45 per cent to 40 per cent, and by three points in Pennsylvania, 46 to 43.

The Republican nominee was doing better among independents in all the three states.

As per RealClearPolitics, which keeps track of all major polls, Clinton was leading Trump by five percentage points in the average of all these polls.

In another poll conducted by HuffPost/YouGov as many as 54 per cent of Republican and party-leaning voters believe Trump isn’t the best choice as the party’s nominee.

On the other hand, 56 per cent of Democratic and Democratic-leaning voters are content with Hillary Clinton as their party’s nominee.

The US presidential election is scheduled for November 8.