The iron ore price jumped again on Tuesday, reaching its highest level since May 15 and adding to 5% gains last week.

The benchmark import price of 62% iron ore fines at China's Tianjin port now trades at $123.70 a tonne according to data supplied by The Steelindex. The rise came after news that China's steel output hit a fresh record high.

China already produces steel at almost the same rate as the rest of the world combined and in late June produced 2.18 million tonnes per day, beating the record set in the first half of the month. At the same time inventories at the country's blast furnaces declined sharply – down almost 7% to 12.6 million tonnes.

On Monday Shanghai rebar, the most actively traded steel futures contract worldwide, declined slightly to 3,575 yuan ($582), not far off a 6-week high and a vast improvement from 2013 lows of $558.

The latest figures indicate that the fundamentals of the Chinese steel industry may not be as dire as previously thought and that iron ore's decline from its February high of close to $160 this year may have been overdone.

The global seaborne iron ore trade is set to hit 1.2 billion tonnes this year and China consumes almost two thirds of that. The SteelIndex reports China’s iron ore imports rose to 65.6 million tonnes in May, according to the latest customs data.