Futures linked to the main U.S. stock averages tick lower, after President Donald Trump rebuffed an Iranian response to an American peace plan as "unacceptable." Oil prices increase following the latest setback to hopes for an immediate resolution to the war in the Middle East. Analysts eye an upcoming trip by Trump to China, and gear up for key inflation data later in the week.

1. Futures slip

U.S. stock futures pointed lower on Monday, as investors assessed the potential for a permanent detente in the Iran war and kept tabs on runaway enthusiasm around artificial intelligence.

By 03:36 ET (07:36 GMT), the Dow futures contract had fallen by 79 points, or 0.2%, S&P 500 futures had slipped by 8 points, or 0.1%, and Nasdaq 100 futures had dropped by 25 points, or 0.1%.

The benchmark S&P 500 and tech-heavy Nasdaq Composite both notched fresh record highs, extending a recent strong run into a sixth consecutive week.

Largely underpinning the gains have been expectations that the Trump administration is searching for a path to conclude a more than two-month war against Iran that has greatly disrupted global flows and threatened the stability of the global economy. At the same time, traders have continued to eye massive ongoing spending by big-name tech companies on the building out of data centers to support AI.

"For stocks stateside, the bull case is simply one that’s too robust to fight right now, as geopolitical optimism combines with stellar earnings growth, and a return of euphoria around the AI theme," said Michael Brown, Senior Research Strategist at Pepperstone, in a note.

"Unless and until any of those factors shift, the path of least resistance should continue to lead higher, with dips remaining relatively shallow for now, and likely being used as buying opportunities by most."

2. Trump rejects Iran counteroffer

According to Iranian state TV, Tehran issued a response to a U.S. plan to end their more than two-month old conflict, focusing on concluding the fighting on all fronts and demanding compensation for war damage.

Iran also stressed that it controlled the Strait of Hormuz, a vital shipping lane off the country’s southern coast through which roughly a fifth of the world’s oil flows. The strait has been all but shuttered during the conflict, and is now blockaded by both the U.S. and Iran.

Writing on social media within hours after Iran appeared to make its counteroffer, Trump said: "I don’t like it — TOTALLY UNACCEPTABLE." No further details were provided.

The U.S. has proposed bringing the war to a swift end, followed by more detailed negotiations on key issues, especially Iran’s nuclear ambitions.

3. Oil rises

Oil prices, which have soared well above pre-war levels and fueled worries over an inflationary spike in countries around the world, marched higher.

Brent crude futures, the global oil benchmark, were last higher by 3.4% at $104.69 a barrel.

"One would expect the market to become increasingly fatigued by the deluge of headlines and the back-and-forth. However, oil prices remain highly sensitive to noise around Iran, highlighting the significance of the ongoing supply disruptions in the Persian Gulf," ING analysts said in a note.

4. Trump to head to China from May 13-15

Still, the strategists suggested that Trump’s upcoming trip to China, a major buyer of Iranian oil, could be positive for peace efforts.

Trump will visit China for a summit with President Xi Jinping between May 13 and 15, Chinese state media reported on Monday.

It will be the first major trip to Beijing by a U.S. leader in nearly a decade, and is aimed at mending strained ties between the world’s largest economies.

Along with the Iran war, Trump and Xi are expected to discuss disputes over trade tariffs and Taiwan. The two are also likely to extend a trade truce signed in October, media reports said.

5. U.S. CPI ahead this week

Looking ahead this week, the U.S. consumer price index is due to highlight a slate of key economic data points.

Set to be released on Tuesday, the figures for April could provide a glimpse into the impact of the Iran war on U.S. inflationary pressures. In March, CPI accelerated, driven mostly by a sharp spike in gasoline-pump prices.

In April, headline consumer prices are seen increasing by 3.7% on an annualized basis, up from 3.3% previously. But, month-on-month, the number is tipped to slow to 0.6% from 0.9%.

So-called "core" CPI, which strips out volatile items like food and fuel, is anticipated to edge up slightly to 0.3% month-on-month. Analysts have been on the lookout for signs that the jump in crude prices will eventually feed into the costs of a range of goods beyond gasoline.