Why has Masjid al-Haram been given a special elevated status compared to other mosques or places of worship in the world?

There are two main reasons as to why Allah has elevated the status of Masjid al-Haram. Firstly, the Qur’an states that Prophet Abraham (alaihi salaam) prayed and asked Allah to bless Makkah as a place of worship. The reason is that he had to go through a test commanded by Allah to leave his wife Hajar and his son Ishmael in a desert. However, Allah blessed that particular circumstance by making Makkah as a centre of commerce in Arabia.

Secondly, Allah commanded Prophet Abraham to build the first house of worship in Makkah, Masjid al-Haram, dedicated to the worship of the One God, Allah. This house of worship was built before the construction of Masjid Al-Aqsa/Bait al-Muqadas. Masjid al-Haram has also been preserved; unlike other structures of worship built by other Prophets. Today, there are no standing structures built by the previous Prophets with the exception of Masjid Nabawi in Medina. Masjid Nabawi was built by the last messenger, our beloved Prophet Muhammad (ﷺ).

Masjid al-Haram has always been persevered, even when people fell into idolatry, and when they made Makkah as a center of idol worship in Arabia. The Prophet Abraham’s prayer for Makkah to remain a purified place was fulfilled by Prophet Muhammad (ﷺ) who made Masjid al-Haram a place solely for the worship of One God and that is Allah alone.

Allah mentions in the Qur’an:

وَإِذِ ٱبۡتَلَىٰٓ إِبۡرَٲهِـۧمَ رَبُّهُ ۥ بِكَلِمَـٰتٍ۬ فَأَتَمَّهُنَّ‌ۖ قَالَ إِنِّى جَاعِلُكَ لِلنَّاسِ إِمَامً۬ا‌ۖ قَالَ وَمِن ذُرِّيَّتِى‌ۖ قَالَ لَا يَنَالُ عَهۡدِى ٱلظَّـٰلِمِينَ

“And [mention, O Muhammad], when Abraham was tried by his Lord with commands and he fulfilled them. [ Allah ] said, "Indeed, I will make you a leader for the people." [Abraham] said, "And of my descendants?" [ Allah ] said, "My covenant does not include the wrongdoers."

 وَإِذۡ جَعَلۡنَا ٱلۡبَيۡتَ مَثَابَةً۬ لِّلنَّاسِ وَأَمۡنً۬ا وَٱتَّخِذُواْ مِن مَّقَامِ إِبۡرَٲهِـۧمَ مُصَلًّ۬ى‌ۖ وَعَهِدۡنَآ إِلَىٰٓ إِبۡرَٲهِـۧمَ وَإِسۡمَـٰعِيلَ أَن طَهِّرَا بَيۡتِىَ لِلطَّآٮِٕفِينَ وَٱلۡعَـٰكِفِينَ وَٱلرُّڪَّعِ ٱلسُّجُودِ 

“And [mention] when We made the House a place of return for the people and [a place of] security. And take, [O believers], from the standing place of Abraham a place of prayer. And We charged Abraham and Ishmael, [saying], "Purify My House for those who perform Tawaf and those who are staying [there] for worship and those who bow and prostrate [in prayer]."

وَإِذۡ قَالَ إِبۡرَٲهِـۧمُ رَبِّ ٱجۡعَلۡ هَـٰذَا بَلَدًا ءَامِنً۬ا وَٱرۡزُقۡ أَهۡلَهُ ۥ مِنَ ٱلثَّمَرَٲتِ مَنۡ ءَامَنَ مِنۡہُم بِٱللَّهِ وَٱلۡيَوۡمِ ٱلۡأَخِرِ‌ۖ قَالَ وَمَن كَفَرَ فَأُمَتِّعُهُ ۥ قَلِيلاً۬ ثُمَّ أَضۡطَرُّهُ ۥۤ إِلَىٰ عَذَابِ ٱلنَّارِ‌ۖ وَبِئۡسَ ٱلۡمَصِيرُ

“And [mention] when Abraham said, "My Lord, make this a secure city and provide its people with fruits - whoever of them believes in Allah and the Last Day." [ Allah ] said. "And whoever disbelieves - I will grant him enjoyment for a little; then I will force him to the punishment of the Fire, and wretched is the destination."

وَإِذۡ يَرۡفَعُ إِبۡرَٲهِـۧمُ ٱلۡقَوَاعِدَ مِنَ ٱلۡبَيۡتِ وَإِسۡمَـٰعِيلُ رَبَّنَا تَقَبَّلۡ مِنَّآ‌ۖ إِنَّكَ أَنتَ ٱلسَّمِيعُ ٱلۡعَلِيمُ

“And [mention] when Abraham was raising the foundations of the House and [with him] Ishmael, [saying], "Our Lord, accept [this] from us. Indeed You are the Hearing, the Knowing.[1]

Abu Dharr reported that he asked, “O Messenger of Allah, which mosque was set up first on the earth?” He replied, “Al-Masjid al-Haram (the sacred).” I then asked, “Then which next?” He replied, “It was the Masjid Al-Aqsa.” I then asked, “How long the space of time (between their setting up)?” He replied. “It was forty years” [2]

References:

[1] Surah al-Baqarah 2:124-127

[2] Saheeh Muslim, 4:1056